please help, i do not understand. thank you!

The marine biologist should select a sample of 38 mahi mahi to estimate the population means within 1.48 pounds with 90% confidence.

To determine the sample size needed for estimating the population mean within a certain margin of error with a 90% confidence level, we can use the following formula:

n = (z*(σ/√n))/E

where:

z = the z-score corresponding to the desired confidence level (in this case, 1.645 for 90%)

σ = the population standard deviation (7.6 pounds)

E = the desired margin of error (1.48 pounds)

n = the sample size

Substituting the given values, we get:

n = (1.645*(7.6/√n))/1.48

Simplifying

n = 3.841n/3.501

n = 1.097n

n ≈ 37.8

Rounding up to the nearest whole number, we get:

n = 38

Therefore, the marine biologist should select a sample of 38 mahi mahi to estimate the population means within 1.48 pounds with 90% confidence.

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Prolongation of the aPTT test can be caused by a clotting factor level less than 40%, indicating potential bleeding disorder or inadequate anticoagulant therapy.

The actuated incomplete thromboplastin time (aPTT) test estimates the time it takes for blood to clump, and it is utilized to screen the viability of anticoagulant treatment or to distinguish draining problems. Prolongation of aPTT shows a lack in at least one coagulating factors.

The base level of a specific thickening element that will cause the aPTT test to become drawn out changes relying upon the particular coagulating factor being tried. Nonetheless, as a rule, a coagulating factor level under 40% is viewed as related with delayed aPTT. Consequently, in the event that the level of a specific thickening component falls underneath 40%, it can cause prolongation of the aPTT test, showing a potential draining problem or a lacking anticoagulant treatment.

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Therefore, the solutions to the equation are x=-2+√3 and x=-2-√3.

The square root of a number is a value that, when multiplied by itself, gives the original number.

For example, the square root of 25 is 5, because 5 x 5 = 25.

The symbol used to represent square root is √.

If you want to find the square root of a number using a calculator or computer, you can use the square root function. For example, the square root of 64 can be found by typing "sqrt(64)" into a calculator, which would give you the answer of 8.

If you want to find the square root of a number by hand, there are a few methods you can use depending on the number. One common method is called the "long division method", which involves breaking down the number into factors and finding the square root of each factor. Another method is called the "guess and check method", which involves making educated guesses and adjusting until you find the square root.

Actually, the last step in your given solution is incorrect. Here are the correct steps to complete the square for the equation. [tex]\sqrt{(x^2+4x+1)}=2:[/tex]

Move the constant term to the right-hand side:

[tex]\sqrt{(x^2+4x)} = 1[/tex]

Add half of the coefficient of x squared to both sides:

[tex]\sqrt{(x^{2} +4x+4)}= 1+2[/tex]

Simplify the perfect square trinomial on the left-hand side and simplify the right-hand side:

[tex]\sqrt{(x+2)^2} = 3[/tex]

Take the square of both sides to eliminate the radical:

[tex]x+2 = \sqrt3[/tex]

Solve for x by subtracting 2 from both sides and considering both the positive and negative square root:

x = -2 ± √3

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Answer:

Okay, I think the answer is D (correct me if I'm wrong, first check others' answers before putting it in)

Step-by-step explanation:

How I got this answer is I remembered that the slope is always the coefficient of x. Because 0.75 is the number next to the variable a for arm length you can assume that is the number the arm length increases for how much the height increases.

Answer: A = 18 in²

Step-by-step explanation:

    To find the area, we will use this formula:

         A = LW

➜ A = Area

➜ L = Length

➜ W = Width

    We will substitute known values and solve by multiplying.

         A = LW

         A = (6 in)(3 in)

         A = 18 in²

The minimum number of customers that need to be included in the test is 1492 members to determine if the new plan has more than a 6% point effect on customer retention, with 90% confidence.

The z-score corresponding to the desired confidence level of 90% = 1.645

The retention rate under the old plan =  1-p = = 0.7

The margin of error = E = 6 percentage points = 0.06

To calculate the minimum number of customers needed for the test, we can use the following formula:

[tex]n = (Z^2 * p * (1-p)) / E^2[/tex]

[tex]n = (1.645^2 * p * (1-p)) / 0.06^2[/tex]

assuming that p = 0.5

n = (1.645^2 * 0.5 * (1-0.5)) / 0.06^2

n = 1492

Therefore we can conclude that the minimum number of customers that need to be included in the test is 1492 members.

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Answer:

Answer: (x + 2.5)² + (y + 4.4)² = 49/16.

Step-by-step explanation:

Answer:

Step-by-step explanation:

pi = 180°

[tex]\frac{17*180}{9} = \frac{3060}{9}= 340[/tex]

The probability that 6 specified arrows hit the target is 0.321.

Probability means how likely an event is to occur. In many real-life situations, we may have to predict the outcome of events. We may or may not be fully aware of the outcome of the event. In this case, we say whether it will happen or not. The result often has good applications in sports, and business as a result of forecasting, and the result is also widely used in the field of new intelligence.

Given that:

She shoot 9 arrows,

the probability of each arrow being fitted 0.6.

Therefore,

The probability that 6 specified arrows hit the target is:

(⁸₄) ×(0.6)⁶ ×(0.4)⁶ = 0.321

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The relationship between length and weight can be modeled by a power function.

The fact that the scatterplot of the natural logarithm of weight vs. the natural logarithm of length shows a more linear relationship suggests that the relationship between length and weight can be better modeled by a power function rather than an exponential function. This is because when the logarithms of both variables are taken, an exponential function becomes a linear function, while a power function remains a non-linear function.

In a power function, one variable is raised to a power that is not necessarily an integer, whereas in an exponential function, one variable is raised to a constant power. Therefore, it is more likely that the relationship between length and weight can be modeled by a power function.

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The amplitude of the sine equation y = 2sin(Θ) - 3 is 6.

What is Graph ?

A graph is a data structure that represents a set of objects and the relationships between them. It consists of a collection of vertices (also known as nodes or points) and a collection of edges (also known as links or arcs) that connect the vertices.

The amplitude of a sine function is the distance between the maximum and minimum values of the function.

From the given graph of y = 2sin(Θ) - 3, we can see that the maximum value of the function is 2 and the minimum value is -4.

Therefore, the amplitude is the absolute value of the difference between the maximum and minimum values:

amplitude = |2 - (-4)| = |2 + 4| = 6

So, the amplitude of the sine equation y = 2sin(Θ) - 3 is 6.

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The statement that cannot be concluded based on the given temperature models is statement 2: "The midline average monthly temperature for Bar Harbor is lower than the midline temperature for Phoenix."

Equations can be simple or complex, and they can involve variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Equations can also be represented graphically using curves or surfaces.

We can compare the two given temperature models to make conclusions about the average monthly temperature variations in Bar Harbor and Phoenix.

First, let's compare the midline temperatures:

Midline temperature for Bar Harbor = 55.300 degrees F

Midline temperature for Phoenix = 86.729 degrees F

Since the midline temperature for Phoenix is higher than that of Bar Harbor, we can conclude that statement 2 cannot be concluded.

Next, let's compare the amplitude of the temperature variations:

Amplitude of temperature variation in Bar Harbor = 23.914 degrees F

Amplitude of temperature variation in Phoenix = 20.238 degrees F

Since the amplitude of temperature variation in Bar Harbor is greater than that of Phoenix, we can conclude that statement 1 is true.

Finally, let's use the temperature models to find the maximum and minimum temperatures:

Maximum temperature in Bar Harbor = 23.914 sin(0.508x-2.116)+55.300

To find the maximum temperature, we need to find the maximum value of the sine function, which is 1. Therefore, the maximum temperature occurs when:

0.508x-2.116 = 90 degrees

Solving for x, we get:

x = (90 + 2.116)/0.508 = 177.066

Plugging this value into the temperature model, we get:

Maximum temperature in Bar Harbor = 23.914 sin(0.508(177.066)-2.116)+55.300 = 78.986 degrees F

Therefore, statement 3 is false.

Minimum temperature in Phoenix = 20.238 sin(0.525x-2.148) + 86.729

To find the minimum temperature, we need to find the minimum value of the sine function, which is -1. Therefore, the minimum temperature occurs when:

0.525x-2.148 = 270 degrees

Solving for x, we get:

x = (270 + 2.148)/0.525 = 517.657

Plugging this value into the temperature model, we get:

Minimum temperature in Phoenix = 20.238 sin(0.525(517.657)-2.148) + 86.729 = 65.983 degrees F

Therefore, statement 4 is false.

Therefore, the statement that cannot be concluded based on the given temperature models is statement 2: "The midline average monthly temperature for Bar Harbor is lower than the midline temperature for Phoenix."

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Statement 2: "The midline average monthly climate for Bar Harbor is less than the midline temperature for Phoenix," cannot be proven based on the provided temperature models.

In addition to variables, constants, and mathematical operations like addition, subtraction, multiplication, division, and exponentiation, equations can be simple or complex. Equations can also be graphically represented using surfaces or curves.

To draw conclusions regarding the average monthly temperature variations in Bar Harbor and Phoenix, we can compare the two provided temperature models.

Let's start by contrasting the midline temperatures:

Midline temperature for Bar Harbor = 55.300 degrees F

Phoenix's midline temperature = 86.729 degrees F

We can infer from the fact that Phoenix's median temperature is greater than Bar Harbor's that assertion 2 cannot be drawn.

Let's compare the temperature variations' amplitude next:

Bar Harbor's temperature variations' severity = 23.914 degrees F

The intensity of Phoenix's temperature variations = 20.238 degrees F

We can infer that assertion 1 is accurate since the amplitude of temperature change in Bar Harbor is bigger than that in Phoenix.

Let's use the temperature models to determine the highest and lowest temperatures.

Bar Harbor's highest temperature is equal to 23.914 sin (0.508x-2.116) + 55.300.

We need to determine the sine function's maximum value, which is 1, in order to determine the maximum temperature. Consequently, the highest temperature is reached when:

0.508x-2.116 = 90 degrees

Solving for x, we get:

x = (90 + 2.116)/0.508 = 177.066

When this value is entered into the temperature model, we obtain:

Bar Harbor's highest temperature record

= 23.914 sin(0.508(177.066)-2.116)+55.300

= 78.986 degrees F

Therefore, statement 3 is false.

Phoenix's low temperature = 20.238 sin(0.525x-2.148) + 86.729

We need to determine the sine function's minimal value, which is -1, in order to determine the minimum temperature. Consequently, the lowest temperature is reached when:

0.525x-2.148 = 270 degrees

Solving for x, we get:

x = (270 + 2.148)/0.525 = 517.657

When this value is entered into the temperature model, we obtain:

Phoenix's low temperature

= 20.238 sin(0.525(517.657)-2.148) + 86.729

= 65.983 degrees F

Therefore, statement 4 is false.

Statement 2: "The midline average month climate for Bar Harbor is lower than the midline temperature for Phoenix," cannot be proved based on the provided temperature models.

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The solution of the given linear inequality will be y ≥ 18.

What are linear inequalities, exactly?

Linear inequalities are mathematical expressions that involve linear functions and the symbols "<", ">", "<=", ">=", or "≠". They are used to describe a range of possible values that a variable can take.

For example, the inequality 3x + 2 > 10 is a linear inequality, where x is a variable. It means that the possible values of x that satisfy the inequality are those that make the expression 3x + 2 greater than 10. The solution set for this inequality is x > 2.

Now,

To solve the inequality y - 6 ≥ 12, we need to isolate y on one side of the inequality sign. We can do this by adding 6 to both sides of the inequality:

y - 6 + 6 ≥ 12 + 6

Simplifying the left side, we get:

y ≥ 18

So the solution set for this inequality is all values of y that are greater than or equal to 18. We can represent this graphically on a number line by shading all values to the right of and including 18:

---|================================>

  18

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Using percentages, we can find that out of the 80 sandwiches sold 16 were salami sandwiches.

Option B is correct.

The denominator of a percentage, also known as a ratio or a fraction, is always 100. For instance, Sam would have received 30 points out of a possible 100 if he had received a 30% on his maths test. Here, "percent" or "percentage" is used to translate the percentage symbol "%." The percent symbol can always be changed to a fraction or decimal equivalent by using the phrase "divided by 100."

Here, the total number of sandwiches sold = 80.

In the chart we can see that out of 80 sold sandwiches, 205 of the sandwiches were salami.

So, 20% of 80

= 20/100 × 80

= 1600/100

= 16.

Therefore, 16 salami sandwiches were sold out of the 80.

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The complete question is:

The deli sold a total of 80 sandwiches. How many salami sandwiches were sold?

4

16

64

20

When (x-5)(x+2) is equal to 0, the value of x can be either 5 or -2.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.

If (x-5)(x+2) is equal to 0, then either (x-5) = 0 or (x+2) = 0, because the product of two factors is equal to 0 only when at least one of them is equal to 0. Therefore, we have:

x - 5 = 0 or x + 2 = 0

Solving these equations for x, we get:

x = 5 or x = -2

Therefore, when (x-5)(x+2) is equal to 0, the value of x can be either 5 or -2.

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The probability of Carlos drawing a blue marble, not replacing it, and then drawing another blue marble is E. 2/15.

The probability of drawing a blue marble on the first draw is 4/10 (since there are 4 blue marbles out of a total of 10 marbles in the bag).

If Carlos does not replace the first blue marble, then there will be 9 marbles left in the bag, of which 3 will be blue. So the probability of drawing another blue marble on the second draw is 3/9.

To find the probability of both events occurring, we multiply the probabilities together:

Probability of drawing a blue marble on the first draw: 4/10

Probability of drawing a blue marble on the second draw, given that the first draw was blue: 3/9

Probability of drawing two blue marbles in a row: (4/10) * (3/9) = 2/15, or approximately 0.133.

Therefore, the probability of Carlos drawing a blue marble, not replacing it, and then drawing another blue marble is approximately 0.133.

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A bag has 6 red and 4 blue marbles. What is the probability Carlos draws a blue marble, does not replace it, and then draws another blue marble?

7/105

6/225

1/35

2/90

2/15

Answer:

The proportion that is false is 18/48 = 30/50.

Step-by-step explanation:

To determine which of the given proportions is false, rewrite the fractions on both sides each equation so that the denominators are the same.

[tex]\dfrac{12}{15}=\dfrac{20}{25} \implies \dfrac{12 \div 3}{15 \div 3}=\dfrac{20 \div 5}{25 \div 5}\implies \dfrac{4}{5}=\dfrac{4}{5}\qquad \boxed{\sf True}[/tex]

[tex]\dfrac{25}{45}=\dfrac{50}{90} \implies \dfrac{25 \div 5}{45\div 5}=\dfrac{50\div 10}{90\div 10}\implies \dfrac{5}{9}=\dfrac{5}{9}\qquad \boxed{\sf True}[/tex]

[tex]\dfrac{20}{50}=\dfrac{40}{100} \implies \dfrac{20\div 10}{50\div 10}=\dfrac{40\div20}{100\div 20}\implies \dfrac{2}{5}=\dfrac{2}{5}\qquad \boxed{\sf True}[/tex]

[tex]\dfrac{18}{48}=\dfrac{30}{50} \implies \dfrac{18\times 25}{48\times 25}=\dfrac{30\times 24}{50 \times24}\implies \dfrac{450}{1200}= \dfrac{720}{1200}\qquad \boxed{\sf False}[/tex]

Therefore, the proportion that is false is 18/48 = 30/50.

Answer: 1/10

1/5 divided by 1/2 = 0.1 = 1/10

Answer:47

Step-by-step explanation:

Check the picture below.

Therefore, we have proved that in parallelogram ABCD, AB is congruent to CD and BC is congruent to DA.

A parallelogram is a four-sided polygon (a flat, closed shape) with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles of a parallelogram are also equal. Parallelograms can have different shapes and orientations, but they always have these defining properties of parallel sides and equal opposite angles and sides. Examples of shapes that are parallelograms include rectangles, squares, and rhombuses.

Given: ABCD is a parallelogram.

Draw diagonal AC.

1. By definition of a parallelogram, BC || DA.

2. By the Unique Line Postulate, there is exactly one line through A that is parallel to BC.

3. By the Reflexive Property of Congruence, AC is congruent to itself.

4. By the definition of alternate interior angles, angle BCA is congruent to angle DAC.

5. By the Alternate Interior Angles Theorem, angle DAC is congruent to angle ZDCA.

6. By the definition of alternate interior angles, angle DCA is congruent to angle ZDCA.

7. By ASA (Angle-Side-Angle) congruence, triangle ABC is congruent to triangle CDA.

8. By CPCTC (Corresponding Parts of Congruent Triangles are Congruent), AB is congruent to CD and BC is congruent to DA.

Therefore, we have proved that in parallelogram ABCD, AB is congruent to CD and BC is congruent to DA.

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Therefore , the solution of the given problem of area comes out to be the picture's revised dimensions are 21 feet long and 15 feet wide.

What is scale factor?

A scale factor is when you enlarge a shape and each side is multiplied by the same number. This number is called the scale factor. Maps use scale factors to represent the distance between two places accurately.

What exactly does an area mean?

Its total size can be determined by figuring out how much area would be required to completely enclose its exterior. When choosing a comparable product for the rectangular design, the surrounding area is taken into account. The total measurements of something are determined by its surface area. The volume of water a cuboid can contain depends on the number in sides between its four trapezoidal shapes.

Here,

The initial image's length and width must be multiplied by 3 in order to enlarge it by a scale factor of 3.

=>  7 feet in length at first.

=>  5 foot original diameter

=> New length = 7ft x 3 = 21ft

=>  New width = 5ft x 3 = 15ft

As a result, the picture's revised dimensions are 21 feet long and 15 feet wide.

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Answer(s):

- miles you drive and the amount of gas in your tank

- the level of water in a water tank being drained over time

Step-by-step explanation:

1. The more miles that you drive, the less gas that is in your tank, so this one has a negative association between its variables.

2. The more time you spend running, the more miles you'll have ran, so that's a positive association, not a negative association.

3. The longer a water tank is drained, the less water it'll have in it, so this one has a negative association between its variables.

4. The speed of a train at a constant speed over the next 6 hours can be modeled by a graph with a horizontal line (which has a slope of zero), representing that as the x increases, the y does not change, so there is not a negative association between the variables.

5. The more cups in the stack, the taller it will be, so that's a positive association, not a negative association.

Answer: Let's assume that the zeros of the given quadratic equation are a and 1/a, since they are reciprocals of each other. By the sum-product relationships for zeros of a quadratic equation, we have:

a + 1/a = -b/a1 = -4/(1-3k) (where b = 4 and a1 = 1-3k)

Multiplying both sides by a1, we get:

a1(a + 1/a) = -4

Expanding the left-hand side, we get:

a1a + a1/a = -4

Multiplying both sides by a, we get:

a1a² + a1 = -4a

Substituting a1 = 1-3k, we get:

(1-3k)a² + (1-3k) = -4a

Rearranging, we get:

(1-3k)a² + 4a + (3k-1) = 0

Since a is one of the zeros of the quadratic, we know that the quadratic can be factored as:

(1-3k)(a - r)(a - s) = 0

where r and s are the other two roots of the quadratic. By expanding the left-hand side, we get:

(1-3k)(a² - (r+s)a + rs) = 0

Comparing with the expanded form of the quadratic, we see that:

r + s = -4/(1-3k)

rs = (3k-1)/(1-3k)

By Vieta's formulas, we know that rs = c/a1, where c is the constant term of the quadratic. Substituting c = -5 and a1 = 1-3k, we get:

rs = -5/(1-3k)

Equating this with the expression we obtained earlier for rs, we get:

-5/(1-3k) = (3k-1)/(1-3k)

Multiplying both sides by 1-3k and simplifying, we get:

-5 = (3k-1)(3k-2)

Expanding the right-hand side, we get:

-5 = 9k² - 15k + 2

Simplifying, we get:

9k² - 15k - 7 = 0

Using the quadratic formula, we get:

k = (15 ± sqrt(15² + 497))/18

k = (15 ± sqrt(429))/18

Therefore, the two possible values of k are:

k = (15 + sqrt(429))/18 ≈ 1.57

k = (15 - sqrt(429))/18 ≈ -0.24

Note that both of these values of k satisfy the condition that the zeros of the quadratic are reciprocals of each other.

Step-by-step explanation:

The constant in the given expression is

C. 9

In a mathematical expression, a constant is a value that does not change and remains the same throughout the expression or equation.

It is a fixed numerical value, coefficient, or term that is independent of the variable(s) in the expression.

For example, in the expression 15x^2 + 2x + 9, the constant is 9, as it remains the same regardless of the value of x.

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The R-square value represents the correct output for the regression models by 71% of the variability in the number of chairs produced can be explained by whether the shift is in the morning or evening and whether it is a weekday shift or weekend shift

The R-square value in regression analysis tells us the proportion of the variability in the response variable.

That can be explained by the regression model.

In this case, the output states that the R-square value is 0.7059.

This means that 70.59% of the variability in the number of chairs produced.

This can be explained by the independent variables in the model which is whether the shift is in the morning or evening and whether it is a weekday or weekend shift.

Therefore, the correct option for the regression model is 'That 71% of the variability in the number of chairs produced can be explained by whether the shift is in the morning or evening and whether it is a weekday shift or weekend shift.'

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The above question is incomplete, the complete question is:

Below is some output from the regression on the furniture factory data. What does the R-square value tell us?

That we cannot reject the null hypothesis

That there is multicollinearity between the independent variables

That on average, 0.7059 more chairs are produced during weekday shifts than during weekend shifts.

That 71% of the variability in the number of chairs produced can be explained by whether the shift is in the morning or evening and whether it is a weekday shift or weekend shift.

The patient's systolic pressure will be the lowest during the time interval 5 < t < 8, when they take the medication at 9 a.m.

The given piecewise function for systolic pressure S(t) has two segments, one for the time interval 5 < t < 8 and another for 8 ≤ t ≤ 12.

For 5 < t < 8, the systolic pressure is a constant value of 115. Therefore, the systolic pressure remains the same during this time interval, and it will not be the lowest.

For 8 ≤ t ≤ 12, the systolic pressure increases linearly with time, starting from 140 and increasing by 9 units every hour. Therefore, the systolic pressure at the beginning of this interval is 140, and it increases until it reaches the maximum value of 211 at t=12.

Since the systolic pressure is highest at the end of the second interval, the lowest value of the systolic pressure must occur in the first interval, which is 5 < t < 8. Therefore, the patient's systolic pressure will be lowest during this time interval, and it will be a constant value of 115.

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The given question is incomplete, the complete question is:

When a patient with hypertension takes a particular type of blood pressure medication, the effects on the systolic pressure, S(t), can be (140-5tif Osts 5 measured by the following piecewise defined function: S(t) = 115 if 5<t<8 - where t is the time, in hours, since 43 +9t if 8sts 12 taking the medication. Based on the graph of the piecewise function, if the patient takes the blood pressure medication at 9 a.m., in which interval will their systolic pressure be lowest?

Once the dimensions of the triangular pyramid are provided, we can perform these calculations to find the volume of the remaining piece in cubic inches.

To determine the volume of the remaining piece, we need to find the volume of the triangular pyramid that was cut off and then subtract it from the original volume of the rectangular prism.

Here are the steps:
Step 1: Determine the volume of the rectangular prism.

The student question already provides this information: 12 cubic inches.
Step 2: Determine the volume of the triangular pyramid.

In order to do this, we need the base area and the height of the pyramid.

However, the diagram is not provided in the question. Please provide the dimensions of the base and height of the triangular pyramid.
Step 3: Calculate the volume of the triangular pyramid using the formula:
Volume = (1/3) × Base area × Height
Step 4: Subtract the volume of the triangular pyramid from the volume of the rectangular prism to find the volume of the remaining piece:
Remaining Volume = Volume of Rectangular Prism - Volume of Triangular Pyramid.

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the particular solution to the given differential equation with the initial condition  [tex]y(pi)=-5[/tex] is: [tex]y = -2 + [(3sec^2(x)-1)/3][/tex]

To find the particular solution to the given differential equation with the initial condition, we can use the method of separation of variables and integrate both sides with respect to x.

Starting with the given differential equation:

[tex]dy/dx = sec^2(x)(2+y)^2[/tex]

We can separate variables and write:

[tex](2+y)^(-2)dy = sec^2(x)dx[/tex]

Integrating both sides, we have:

[tex](2+y)^(-1) = tan(x) + C[/tex]

where C is an arbitrary constant of integration.

To find the value of C, we can use the initial condition y(pi)=-5:

[tex](2+(-5))^(-1) = tan(pi) + C[/tex]

[tex](2-5)^(-1) = 0 + C[/tex]

[tex]C = -1/3[/tex]

Substituting this value of C back into the general solution we obtained earlier, we get:

[tex](2+y)^(-1) = tan(x) - 1/3[/tex]

Multiplying both sides by  [tex](2+y)[/tex] , we can solve for y:

[tex]y = -2 ± [(3sec^2(x)-1)/3][/tex]

Therefore, the particular solution to the given differential equation with the initial condition   [tex]y(pi)=-5[/tex] is: [tex]y = -2 + [(3sec^2(x)-1)/3][/tex]

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